Question 106
(a) Suppose $n=k^2$ is a perfect square. Prove that the number of positive divisors of $n$ below $k$ equals the number above $k$.
(b) Prove that $k^2$ has at most $2k-1$ positive divisors.
(c) Find every positive integer $k$ for which $k^2$ has exactly $2k-1$ positive divisors.
(b) Prove that $k^2$ has at most $2k-1$ positive divisors.
(c) Find every positive integer $k$ for which $k^2$ has exactly $2k-1$ positive divisors.